Portfolio construction is enabled through the multi objective optimization. The nature of the problem invites the construction through multi objective optimization. Genetic algorithm and the particle swarm optimization is used for the above purpose. The results obtained are compared against the classical Markowitz model. The data from the Nifty from March 2010 to October 2010 has been used. The Stocks from various sectors are used to build the portfolio. The proposed work is promising and the results obtained are outperforming. Comparing on both the algorithms PSO based multi objective optimization serves better than Genetic algorithms based on the results obtained.

Portfolio Optimization; MOPSO; MOGA

[1] Zadeh LA, “Optimality and non-scalar-valued
performance criteria”, IEEE Trans Automat
Contr, (1963)AC-8:59–60.
[2] Koski J, Silvennoinen R, “Norm methods and
partial weighting in multicriterion optimization of
structures”, Int J Numer Methods Eng, (1987),
24:1101–1121.
[3] R. Timothy Marler • Jasbir S. Arora, “The
weighted sum method for multi-objective
optimization: new insights”, Struct Multidisc
Optim, springer, (2010), 41:853–862.
[4] Marler RT, Arora J S, “Transformation methods
for multiobjective optimization”, Eng Optim,
(2005), 37:551–569.
[5] Ching-Lai Hwang; Abu Syed Md Masud,
“Multiple objective decision making, methods
and applications: a state-of-the-art survey”,
Springer-Verlag, (1979).
[6] Zeleny, M, "Compromise Programming", in
Cochrane, J.L.; Zeleny, M., “Multiple Criteria Decision Making”, University of South Carolina Press, Columbia, (1973), pp. 262–301.
[7] http://en.wikipedia.org/wiki/Multi-
objective_optimization.
[8] Das, I.; Dennis, J. E. (1998). "Normal-Boundary
Intersection: A New Method for Generating the
Pareto Surface in Nonlinear Multicriteria
Optimization Problems", SIAM Journal on
Optimization 8 (3): 631.
doi:10.1137/S1052623496307510.
[9] S. Motta, Renato; Afonso, Silvana M. B.; Lyra,
Paulo R. M. (8 January 2012), "A modified NBI
and NC method for the solution of N-
multiobjective optimization problems",
Structural and Multidisciplinary Optimization.
doi:10.1007/s00158-011-0729-5.
[10] Messac, A.; Ismail-Yahaya, A.; Mattson, C.A.
"The normalized normal constraint method for
generating the Pareto frontier", Structural and
multidisciplinary optimization, (2003). 25
(2): 86–98. doi:10.1007/s00158-002-0276-1.
[11] Messac, A.; Mattson, C. A,"Normal constraint
method with guarantee of even representation of
complete Pareto frontier". AIAA journal 42
(10): 2101–2111, (2004), doi:10.2514/1.8977.
[12] Mueller-Gritschneder, Daniel; Graeb, Helmut;
Schlichtmann, Ulf "A Successive Approach to
Compute the Bounded Pareto Front of Practical
Multiobjective Optimization Problems", SIAM
Journal on Optimization 20 (2): 915–934,
(2009), doi:10.1137/080729013.
[13] Erfani, Tohid; Utyuzhnikov, Sergei V, "Directed
Search Domain: A Method for Even Generation
of Pareto Frontier in Multiobjective
Optimization", Journal of Engineering
Optimization 43 (5): 1–18, (2011), Retrieved
October 17, 2011.
[14] Miettinen, K.; Ruiz, F.; Wierzbicki, A. P,
"Introduction to Multiobjective Optimization:
Interactive Approaches". Multiobjective
Optimization. Lecture Notes in Computer Science
5252, 2008.
[15] Luque, M.; Ruiz, F.; Miettinen, K, "Global
formulation for interactive multiobjective
optimization", OR Spectrum 33: 27, 2008,
doi:10.1007/s00291-008-0154-3.
[16] Ruiz, F.; Luque, M.; Miettinen, K. (2011),
"Improving the computational efficiency in a
global formulation (GLIDE) for interactive
multiobjective optimization", Annals of
Operations Research 197.
[17] Veldhuizen, D; Lamont, G, "Multiobjective
Evolutionary Algorithms: Analyzing the State-
of-the-Art," Evolutionary Computation , vol.8,
no.2, June 2000,pp.125,147.
[18] Goldberg, D.E., & Deb, K.,“A comparative
analysis of selection schemes used in genetic
algorithms”. In G.J.E. Rawlins (Ed.),
Foundations of genetic algorithms, (1991),
pp. 69-93.
[19] Carlos A. Coello Coello, A Short Tutorial on
Evolutionary Multiobjective Optimization,
http://www.cs.bham.ac.uk/~durranrj/NID/
documentCache /tutorial1/tutorial-slides-
coello.pdf, 2001.
[20] http://www.iitmandi.ac.in/ciare/files/8
Ashwani _MOGA.pdf.
[21] http://eden.dei.uc.pt/~cmfonsec/fonseca-ec-
v3n1-preprint.pdf.
[22] Jones, D.F., Mirrazavi, S.K., and Tamiz, M., “
Multiobjective meta-heuristics: an overview of
the current state-of-the-art”, European Journal of
Operational Research 137(1) (2002) 1-9.
[23] http://ie.rutgers.edu/resource/research_paper
/paper_05-008.pdf
[24] Schaffer, J.D, “Multiple Objective optimization
with vector evaluated genetic algorithms”,
International Conference on Genetic
Algorithm and their applications . 1985.
[25] Fonseca, C.M. and Fleming, P.J,
“.Multiobjective genetic algorithms”, In IEE
Colloquium on `Genetic Algorithms for Control
Systems Engineering' (Digest No. 1993/130),
28 May 1993 .
[26] Horn, J., Nafpliotis, N., and Goldberg, D.E, “ A
niched Pareto genetic algorithm for
multiobjective optimization” , In Proceedings
of the First IEEE Conference on Evolutionary
Computation. IEEE World Congress on
Computational Intelligence, 27-29 June 1994.
[27] Murata, T. and Ishibuchi, H., “MOGA : multi-
objective genetic algorithms”, In Proceedings of
1995 IEEE International Conference on
Evolutionary Computation, 29 Nov.-1 Dec.
1995.
[28] Srinivas, N. and Deb, K., “Multiobjective
Optimization Using Nondominated Sorting in
Genetic Algorithms”,Journal of Evolutionary
Computation 2(3) (1994) 221-248.
[29] Zitzler, E. and Thiele, L., “Multiobjective
evolutionary algorithms: a comparative case
study and the strength Pareto approach”, IEEE
Transactions on Evolutionary Computation 3(4)
(1999) 257-271.
[30] Knowles, J.D. and Corne, D.W.,
“Approximating the nondominated front using
the Pareto archived evolution strategy”,
Evolutionary Computation 8(2) 149-172.
[31] Deb, K., Pratap, A., Agarwal, S., and Me
yarivan, T., “A fast and elitist multiobjective
genetic algorithm: “, NSGA-II, IEEE
Transactions on Evolutionary Computation 6(2)
(2002) 182-197.
[32] Sarker, R., Liang, K.-H., and Newton, C, “A
new multiobjective evolutionary algorithm”,
European Journal of Operational Research
140(1) (2002) 12-23.
[33] Lu, H. and Yen, G.G., “Rank-density-based
multiobjective genetic algorithm and benchmark
test function study”, IEEE Transactions on
Evolutionary Computation7(4) (2003) 325-343
[34] http://www.cc.gatech.edu/~bhroleno/cs6601
/mopso.pdf
[35] J. Kennedy and R. C. Eberhart, “Swarm
Intelligence”, San Mateo, CA: Morgan
Kaufmann, 2001.
[36] Carlos A. Coello Coello, “Handling Multiple
Objectives With Particle Swarm Optimization”,
IEEE Transactions On Evolutionary
Computation, Vol. 8, No. 3, June 2004.
[37] Margarita Reyes-Sierra and Carlos A. Coello
Coello,” Multi-Objective Particle Swarm
Optimizers: A Survey of the State-of-the-Art”,
2006.
[38] Eduardo J. Solteiro Pires 1, Jos´e A. Tenreiro
Machado and Paulo B. de Moura Oliveira,
“Entropy Diversity in Multi-Objective Particle
Swarm Optimization”, Entropy 2013, 15, 5475-
5491.
[39] Mishra, S.K.; Panda, G.; Meher, S.; Majhi, R.;
Singh, M., "Portfolio management assessment
by four multiobjective optimization algorithm,"
Recent Advances in Intelligent Computational
Systems (RAICS), 2011 IEEE, vol., no, Sept.
2011, pp.326,331, 22-24.
[40] http://homepages.rpi.edu/~bonisp/NASA-course
/cec05.pdf
[41] http://thesis.topco-global.com/TopcoTRC
/2010_Thesis/B0022.pdf
[42] I. Radziukynienė , A. Žilinskas, “Evolutionary
Methods for Multi-Objective Portfolio
Optimization”, Proceedings of the World
Congress on Engineering 2008 Vol II.